Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 1.75% per annum.
- UNH price at the close of May 1, 2025 was $400.68 and was lower than the bottom border of the primary price channel by $57.46 (12.54%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 27.51% per annum.
- UNH price at the close of May 1, 2025 was lower than the bottom border of the secondary price channel by $34.40 (7.91%).
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of UNH price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: December 6, 2021
End date: July 15, 2024
a = 6.1378
b = 0.0000
s = 0.0486
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0486) – 1
= 21.46%
December 6, 2021 calculations
Top border of price channel:
Exp(Y402)
= Exp(a + b × X402 + 2 × s)
= Exp(a + b × 581 + 2 × s)
= Exp(6.1378 + 0.0000 × 581 + 2 × 0.0486)
= Exp(6.2626)
= $524.58
Bottom border of price channel:
Exp(Y402)
= Exp(a + b × X402 – 2 × s)
= Exp(a + b × 581 – 2 × s)
= Exp(6.1378 + 0.0000 × 581 – 2 × 0.0486)
= Exp(6.0682)
= $431.89
July 15, 2024 calculations
Top border of price channel:
Exp(Y1,055)
= Exp(a + b × X1,055 + 2 × s)
= Exp(a + b × 1,533 + 2 × s)
= Exp(6.1378 + 0.0000 × 1,533 + 2 × 0.0486)
= Exp(6.3078)
= $548.85
Bottom border of price channel:
Exp(Y1,055)
= Exp(a + b × X1,055 – 2 × s)
= Exp(a + b × 1,533 – 2 × s)
= Exp(6.1378 + 0.0000 × 1,533 – 2 × 0.0486)
= Exp(6.1134)
= $451.87
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.75% per annum.
- UNH price at the close of May 1, 2025 was $400.68 and was lower than the bottom border of the primary price channel by $57.46 (12.54%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: August 13, 2024
End date: March 28, 2025
a = 7.7776
b = -0.0009
s = 0.0475
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -27.51%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0475) – 1
= 20.94%
August 13, 2024 calculations
Top border of price channel:
Exp(Y1,076)
= Exp(a + b × X1,076 + 2 × s)
= Exp(a + b × 1,562 + 2 × s)
= Exp(7.7776 + -0.0009 × 1,562 + 2 × 0.0475)
= Exp(6.4957)
= $662.30
Bottom border of price channel:
Exp(Y1,076)
= Exp(a + b × X1,076 – 2 × s)
= Exp(a + b × 1,562 – 2 × s)
= Exp(7.7776 + -0.0009 × 1,562 – 2 × 0.0475)
= Exp(6.3056)
= $547.64
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 + 2 × s)
= Exp(a + b × 1,789 + 2 × s)
= Exp(7.7776 + -0.0009 × 1,789 + 2 × 0.0475)
= Exp(6.2956)
= $542.19
Bottom border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 – 2 × s)
= Exp(a + b × 1,789 – 2 × s)
= Exp(7.7776 + -0.0009 × 1,789 – 2 × 0.0475)
= Exp(6.1055)
= $448.32
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 27.51% per annum.
- UNH price at the close of May 1, 2025 was lower than the bottom border of the secondary price channel by $34.40 (7.91%).
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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